That's an interesting idea. I haven't used an ensemble so i don't really know what options there are for you....
Personally I'd create a template with which you can easily switch to outputs 3-4 as your headphones output or select and solo the rhythmic tracks and the tracks you want to record and go that way....
If you go the sends to an aux route then with multiple channel strips selected you can Option click on the send to disable them all. A few key commands and really speed up the process.
New monitors will always colour the sound in some way - or perhaps accentuate certain frequencies.
In fact, now thinking about this more, you can send to multiple busses and with the aux's created solo the aux's you want to monitor. In essence it's similar to producing stem mixes (routing the drums to aux 1, the keys to aux 2, the guitars to aux 3 etc etc...). Except you could route say, tracks 1 to 10 to aux 1. Tracks 1,2,7,8,9 to aux 2. Tracks 3,4,5,6,7 to aux 3 etc etc. Then just solo the aux you want to listen to. These aux's could be set to output 1-2 only or a combination of 1-2 and 3-4 depending on whether you want to use different monitors or not.
Does that sound like an option?